图的拓扑排序

对一个有向无环图(Directed Acyclic Graph简称DAG)G进行拓扑排序，是将G中所有顶点排成一个线性序列，使得图中任意一对顶点u和v，若边<u,v>∈E(G)，则u在线性序列中出现在v之前。通常，这样的线性序列称为满足拓扑次序(Topological Order)的序列，简称拓扑序列。简单的说，由某个集合上的一个偏序得到该集合上的一个全序，这个操作称之为拓扑排序。

参考1：https://www.bilibili.com/video/BV1uf4y1U7DX?from=search&seid=6563497796764449577

参考2：https://www.runoob.com/python3/python-topological-sorting.html

from collections import defaultdict


class Graph:
    def __init__(self, vertices):
        self.graph = defaultdict(list)
        self.V = vertices

    def addEdge(self, u, v):
        self.graph[u].append(v)

    def topologicalSortUtil(self, v, visited, stack):

        visited[v] = True

        for i in self.graph[v]:
            if visited[i] == False:
                self.topologicalSortUtil(i, visited, stack)

        stack.insert(0, v)

    def topologicalSort(self):
        visited = [False] * self.V
        stack = []

        for i in range(self.V):
            if visited[i] == False:
                self.topologicalSortUtil(i, visited, stack)

        print(stack)


g = Graph(6)
g.addEdge(5, 2);
g.addEdge(5, 0);
g.addEdge(4, 0);
g.addEdge(4, 1);
g.addEdge(2, 3);
g.addEdge(3, 1);

print("拓扑排序结果：")
g.topologicalSort()